A source of sound waves at frequency 1.0 kHz is traveling through the air at .5 times the speed of sound?

a.)find the frequencey of the sound recieved by a stationary observer if the source moves toward her
b.) repeat if the source moves away from her instead

The Doppler shift of the frequency, when source moves towards resting observer, is given by:
f = f₀·( c / (c - v)) = f₀ / (1 - v/c)
f₀ frequency at source, v speed of the source, c speed of waves

For opposite direction of motion change sign in denominator

a)
f = 1kHz / (1 - 0.5) = 2kHz

b)
f = 1kHz / (1 + 0.5) = (2/3)kHz = 0.667kHz